Abstract A finite CW-complex X is called P P -trivial if, for any real vector bundle ξ over X, the total Pontrjagin class p (ξ) = 1. In this article, we completely determine when each of the following spaces are P P -trivial: suspensions of stunted real projective spaces, suspensions of stunted complex projective spaces. Furthermore, we show that the 3-fold suspension of a compact orientable surface of genus ≥ 1 1 is not P P -trivial.
Podder et al. (Thu,) studied this question.